Bullet hell is where enormous amounts of bullets are fired at the player by relatively few enemies, requiring lots of memorisation and twitch reaction skill to avoid the fast and complex patterns that fill the screen. It is intentionally extremely challenging. eg. https://youtu.be/aosBBHSZE-A?si=-Wn-aMPPbFXtcKNr&t=802

Bullet heaven is where enormous amounts of enemies swarm a player who has ridiculous firepower to take out dozens of enemies at the same time, requiring little more than circle strafing and holding the fire button. It is intentionally casual, and the gameplay is about the RPG/roguelike upgrading aspect much more than the actual game mechanics. eg. https://www.youtube.com/watch?v=V8TiJY3lXmQ

If you want a critical take of the difference between the two, and the direction of the games market from a shmup-fan’s perspective, I found this review by The Electric Underground really interesting: https://www.youtube.com/watch?v=HSS_3iTIgA4 (it obviously predates this Steam label change, so there is some hand-wringing about what is being classified as bullet-hell).